Sur le théorème de Poincaré-Bendixson

Measure preserving pseudo-groups and a theorem of Sacksteder

“…Remark. -(6.2) is an improvement over the corresponding results in [3] and [6] in that it is not necessary to assume that the individual leaves of ^ are immersed submanifolds of class C 3 . 1) The orbits of 0^.…”

“…In [7,8] Sacksteder proved a generalization of Denjoy's result which has been extensively exploited by authors studying codimension one foliations. For example, in [3] and [6] it is shown that C 2 codimension one foliations whose leaves have non exponential growth cannot have exceptional minimal sets. The proof uses Sacksteder's theorem as well as the generalization for codimension one foliations of the Poincare-Bendixson theorem.…”

Sur l'invariance topologique de la classe de Godbillon-Vey

“…La signification géométrique de ces classes secondaires et, en particulier, de l'invariant de Godbillon-Vey, reste cependant assez peu claire. R. Moussu et F. Pelletier d'une part [20], et D. Sullivan d'autre part [23], suggèrent alors que cet invariant pourrait être de nature dynamique et, dans cet esprit, conjecturent qu'un feuilletage à croissance sous-exponentielle (i.e. « dynamiquement simple ») a un invariant de Gôdbillon-Vey trivial.…”

Classifying foliations

“…Notable advances included Hector's work on classification and examples, starting with his Thesis and subsequent developments of its themes [132,133,135,138]; Lamoureux's work on holonomy and "captured leaves" [200,201,202,203]; Moussu's study of foliations almost without holonomy [239,240]; Nishimori's study of the asymptotic properties and growth of leaves in foliations [245,246,247,248]; and Plante's study of the relation between growth of leaves and the fundamental groups of the ambient manifolds.…”